Problem: Simplify the following expression and state the condition under which the simplification is valid: $n = \dfrac{r^2 + 5r}{r^2 - 25}$
Answer: First factor the expressions in the numerator and denominator. $ \dfrac{r^2 + 5r}{r^2 - 25} = \dfrac{(r)(r + 5)}{(r - 5)(r + 5)} $ Notice that the term $(r + 5)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(r + 5)$ gives: $n = \dfrac{r}{r - 5}$ Since we divided by $(r + 5)$, $r \neq -5$. $n = \dfrac{r}{r - 5}; \space r \neq -5$